The NFHS rules book covers the Code Of Ethics of coaches. Specifically it states.

"The coach shall not seek an advantage by circumvention of the spirit or letter of the rules."

As it pertains to the use of such devices. Each competitor is allowed up to two injury time-outs per match. How they do so is at their discretion.

By and large officials are not doctors, and even the ones that are aren't in the business of diagnosing or making a medical determination on the spot in a wrestling event. You can't even begin to understand the liability risk an official would place onto themselves by denying a competitors request for an injury time-out whether it's legitimate or not.

There is absolutely no need to have this discussion at all. If a kid or his coach wants an injury time out it must be granted. The reasons for such a request are irrelevant. It is not a rabbit hole you really want to go down.